Date: Feb 3, 2013 4:13 PM
Author: Virgil
Subject: Re: Matheology � 203

In article 
WM <> wrote:

> On 3 Feb., 09:26, William Hughes <> wrote:
> > On Feb 3, 8:51 am, WM <> wrote:
> >
> > > In fact we can say that in a suitable list "every" initial segment of
> > > s is contained in some line, since there is no s(n) = (s1, s2, ...,
> > > sn) missing. But there is no sensible way of saying "all" initial
> > > segment.

> >
> > We can say "every line has the property that it
> > does not contain every initial segment of segment of s"
> > There is no need to use the concept "all".

> Yes, and this is the only sensible way to treat infinity. But "every
> initial segment" has, inadvertently and only noticed by sharp minds
> like those of Brouwer and Weyl, changed into "all initial segments" as
> you can see from the question concerning the path of 1/3 in a Binary
> Tree that contains only every initial segment of the path of 1/3.

If it is actually a path in a CIBT, meaning that it has an actual
inifinity of nodes, then it contains not only every but also all finite
initial segments of the binary form of 1/3
> Set theory exists only because of the continued switching between
> these two meanings. If I ask for a level omega distinguishing between
> "every finite path" and the "actually infinite path", I am railed at
> (with full right - a level omega is nonsense). But by sending terms of
> a sequence only, information about an infinite sequence has never been
> transferred.

If one gives a general form for those terms, one defines ALL of them

In binary, 1/3 is 0.(01), where (01) indicates the infinite string of 01
repeating forever.

And every of actually infinitely many proper fractions has has some
finitely expressible binary expression.